vol. xxxvi, issue 4 december 2015 president’s · vol. xxxvi, issue 4 december 2015 president’s...
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BULLETIN®
December 2015Vol. XXXVI, Issue 4
President’s MessageDecember 2015 by George Reese, ICTM President
Mission: Illinois Council of Teachers of Mathematics is a community of PreK through Post-graduate (PreK–20) educators promoting equitable, high quality mathematics teaching and learning through leadership, collaboration, advocacy and professional development.
Vision: The Illinois Council of Teachers of Mathematics is the state leader in mathematics education. ICTM is committed to sound pedagogy, teacher collaboration, and professional development, ensuring student achievement through engagement in meaningful and rigorous instruction. As a respected leader in mathematics education at the school, district, state, and national levels, ICTM serves as a collaborative partner to promote the achievement of every student.
Looking Ahead After a Great Conference
October’s Annual Conference was a
wonderful opportunity to be re-invigorated by the comradery and pure joy of being around friends and colleagues. Our keynote speakers were wonderful. Two new items on my holiday to-do list are to spend more time with Desmos and to get Jo Boaler’s new Mathematical Mindsets. It seems to me that Eli Luberoff and Jo Boaler both emphasized the joy of taking risks, making mistakes, and having fun as we work. I will long remember Dr. Boaler saying after an hour of her presentation, “I want us to do some math now, which makes me happy.” The conference committee did a wonderful job in getting us these fine keynoters and organizing the program. This year’s conference saw some new offerings: for the first time there was a poster session and a job fair. The poster session featured 10 posters with a range of topics from Mathematics and Social Justice to Tiling and Tessellation. Many thanks to the presenters, most of whom were students, for helping us get started with this new format. We hope to grow it next year. Both the poster session and the job fair were ideas of ICTM President, now-Past President, Bob Mann. His creative energy and careful diplomacy helped smooth the bumps and keep energy high as we traversed new territory with this conference. One major change this year was the presence of the Illinois Science Teachers Association (ISTA),
whose conference happened in parallel to ours. Most of the comments that I heard were positive regarding the dual conference format, especially the number of exhibits that ISTA brought with them to Tinley Park. The 2016 Conference will be in Peoria, and we hope to have some sessions there that combine mathematics and science.
As we look forward, not just to the next conference, but to the many events that ICTM sponsors and endorses throughout the year, we will need to address some challenges as well. How can our organization become a more diverse community of mathematics educators and learners? How can we make optimal use of new technologies for communication and collaboration? How can we provide additional value to all our members and their students? These are questions with which I know the ICTM Board of Directors will continue to wrestle, and we will need the help of the membership to get the answers right. Please use the Website, the ICTM listserv, and your connections to individual Board members to communicate your hopes and constructive criticisms. As teachers, I hope we will also be good listeners.
George ReeseICTM [email protected]
In This Issue:Articles of InterestPresident’s Message p. 1Past President’s Message p. 2Board Chair Report p. 2ICTM Awardees and p. 4-5 Scholarship RecipientsICTM Board Members p. 10
Classroom ActivitiesIntroduction to KenKen Puzzles p. 7 (Grades 2-12)Share and Share Alike? p. 8-9 (Grades 9–12)
Information to ShareRegional Conferences p. 3 ListServe Update p. 3NCTM Reminder p. 3Math Musings... p.3 2015 Conference Corner p. 6ICTM Membership Application p. 11
Calls for InformationScholarship Nominations p. 4Award Nominations p. 4Call for Speakers p. 6Call for Articles p. 10
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Board Chair Reportby Jackie Murawska, ICTM Board Chair
Greetings ICTM members! My name is Jackie Murawska and I teach mathematics at Saint Xavier University in Chicago. I’m excited to be your new Board Chair for 2015-16. At the August 22, 2015 Board meeting, we expressed gratitude to our three outgoing board members—Kara Leaman, Adam Poetzel, and Jennie Winters—for their substantial contributions to ICTM. Both Rich Wyllie and Lannette Jennings will gratefully continue in their
positions as treasurer and secretary, respectively. We also welcomed three new board members:
• Jeremy Babel, Director 9-12• Denise Brown, Director EC-6 • Sendhil Revuluri, Director At Large
Most of the board’s time at the last meeting was spent on the ICTM Annual Conference. We discussed the affiliate luncheon, business meeting, student volunteers, interview fair, poster session, and maximum participants due to space limitations. The board approved a complimentary breakfast on Saturday for all conference attendees. Much discussion ensued about re-evaluating contracts with different vendors for conference registration, publication, and membership. A motion was approved for a subset of Board members to investigate options for contracting membership management.
In addition, the board discussed in detail the status of conference preparation thus far with the Illinois Science Teachers Association (ISTA), as 2015 was the first year that ICTM and ISTA held their conferences concurrently in the same venue. Discussion included planning, financial factors, and potential advantages of having a co-conference or a joint conference, and possible effects on membership and conference attendance. Next year’s ICTM Annual Conference will be held October 7-8, 2016 in Peoria, Illinois. Marshall Lassak, Conference Chair, will be heading up the conference team to plan the event. Lastly, the Board also discussed nominations procedures, ways to encourage listserve subscribers to become members, and updates on the ISBE Model Math Curriculum. The Publication liaison position was changed to a Media and Publications committee, and the new liaison responsibilities are listed below. Please feel free to contact any of these Board members if needed.
Liaison Responsibility Name EmailAffiliates Craig Cullen [email protected] Updates Jennie Winters [email protected] Eric Bright [email protected] Eric Bright [email protected] Relations Carly Morales [email protected] Peter Wiles [email protected] Repsresentative Jackie Murawska [email protected] Anita Reid
Martin [email protected]@newtrier.k12.il.us
Scholarships Randy and Sue Pippen [email protected] Adam Poetzel [email protected] – Mathematics & Science Parnerships
Jennie Winters [email protected]
The next Board meeting will be held at the Bloomington Holiday Inn Express and is scheduled for December 5, 2015.
Happy Holidays Math Fans!
I hope the season blesses you with productive classrooms and fun festivities. I believe this year’s conference was both productive
and fun and I want to thank all of you who attended and presented at this event. I also want to thank the conference team, led for 28 years now by Ann Hanson, the ICTM board, the many volunteers, and ISTA leaders for helping make the 65th annual conference a success. The past two years have seen many changes in our conference format and design and it took the work of many talented and dedicated individuals to make it all work—thank you all very much!
As a reminder, conference resources and session materials can still be found at http://www.ictm.org/annualmeeting/SessionResources.asp. We hope you find this resource and the other ideas and materials at www.ictm.org valuable for you and your students.
Next year’s conference will be Oct. 7 and 8 in Peoria and again should provide tremendous opportunities for networking and for high-quality professional development. I encourage you now to mark those dates on your 2016 calendar and to consider presenting at our 66th annual conference. We will again be working with ISTA to provide mathematics and science sessions at the same venue and I expect that the venue will again be alive with energy, excitement, and enrichment—so plan now on ICTM 2016!
In the meantime, keep in touch with ICTM on our website, facebook page, list serve, and via twitter (#ICTM2016) and keep your synapses snapping, your Desmos dazzling, and your mindset (and that of your students) growing! Have a fantastic 2016!
Past President’s Messageby Bob Mann ICTM Past President
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ICTM Listserv Update
Do you receive e-mails from the ICTM Listserv?
If you answered no, then consider subscribing today. Subscription to the Listserv is a benefit of your ICTM membership. E-mails sent through the Listserv often give information about upcoming conferences, details about professional development opportunities, information about ICTM awards and scholarships, links to math related websites and news articles, and questions/announcements from other math teachers around the state. All subscribers to the Listserv can send out messages to the recipient list. To sign up, visit www.ictm.org/ListServe.htm and complete the short online form. You can choose to unsubscribe from the List Serve at any time. Subscribe today and join the conversation!
NCTM Reminder:Help your professional organizations support each oth-er! When renewing your National Council of Teach-ers of Mathematics Membership online, don’t forget to checkmark the Affilate Rebate box and designate ICTM as your affiliate organization. NCTM’s Affiliate Rebate program provides a per-member rebate to ICTM based on this feedback. Your attention to this detail helps pro-vide support for your local professional organization.
Math Musingswith Martin
Q: Of the ten numbers with both motive and oppor-tunity, the police only brought in 7, 5, 3, and 2 for
questioning. Why?
A; They were the prime suspects
Submitted by Martin Funk, ICTM Director 9–12
PLANNOW:
ATTEND YOUR LOCAL ICTM
Regional ConferenceSIU-Carbondale
ThursdayFebruary 18, 2016For more information, contact:
WIU-MacombFriday
April 8, 2016For more information, contact:
www.wiu.edu/cas/math/teachers_conference
Illinois Mathematics Teacher Journalcall for articlesThe editors invite submissions from both new and experienced authors, and accept articles on a range of topics, including:
• innovative classroom activities and lessons• applications to the classroom of pedagogical
research and best practices• examples of implementing standards• reviews of recent books on pedagogy • any other articles that will support the
professional development of ICTM members
Please send submissions to [email protected].
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Friday afternoon, October 23, many Illinois mathematics teachers had a wonderful experience as the ICTM awards were presented. The recipients were recognized by their colleagues for their excellence, and those in attendance were able to affirm what it means to be a truly outstanding educator. Once again, it was inspiring to experience the good feelings that went out to these distinguished colleagues.
Now it is time to identify the next group of award winners for 2016. The first step in the process is nomination. That requires a few people to take the time to identify the strengths and contributions of someone that they work with or someone who has taught them or their children. The sad part of this year’s award ceremony was that no one received the outstanding elementary math teacher or outstanding post-secondary teacher award because no one was nominated for either. I know there are many deserving teachers. So do you. Please take the time to help them get the recognition they deserve. Instructions for nomination are on the ICTM web site. Nominations do not need to be submitted until the last day in March, 2016, but now is a good time to decide who you are going to nominate and get organized to do it. If you nominated someone in the past who is still eligible for the award, and that person did not get the award, all you need to do is ask us to reactivate the nomination. You can add to it if you
like. Many of the recipients of recent awards were nominated in previous years and did not get the award at that time.
ICTM AWARDS AVAILABLE• Elementary Mathematics Teaching Award• Middle School Mathematics Teaching Award• T.E. Rine Secondary Mathematics Teaching Award• Post-Secondary Mathematics Teaching Award• Max Beberman Mathematics Educator Award• Lee Yunker Mathematics Leadership Award• Distinguished Life Achievement in Mathematics Award• Illinois Promising New Teacher of Mathematics Award• Fred Flener Award: Engaging Students in Mathematics Beyond the
Classroom
Specific award criteria and application forms can be found on the ICTM website, at www.ictm.org. With your help, ICTM can continue to recognize excellent mathematics educators in Illinois!
Award application deadline is March 31, 2016John Benson and Eric Bright
As Scholarship Co-Chairs, one of our favorite things to do is give away scholarships to promising young mathematics teachers either in their first year of teaching or their senior year in college. They apply in the spring while they are still juniors or seniors if they are mathematics majors or elementary education majors with a concentration in mathematics.
This year we awarded $1500 each to Maria Christina Gianni from the University of Illinois at Champaign-Urbana teaching her first year at Gombert Elementary in Aurora, and Amy Wieting from Illinois State University where she is a senior. These deserving young ladies show a great deal of potential to become future ICTM stars.
The scholarship committee would like to thank everyone who donated to the scholarship fund as well as members who assisted in collecting donations. Without your support, ICTM could not give these awards to deserving college junior and seniors. We also would like to thank our readers who help evaluate the applications.
If you did not donate and would like to, please send a check payable to ICTM Scholarship. The check can be mailed to Sue and Randy Pippen, 24807 Winterberry Lane, Plainfield, IL 60585.
Applications for scholarships may be made by visiting www.ictm.org and click on scholarship. All application information and forms are downloadable. Please reach out and encourage college juniors and seniors to apply for the ICTM Scholarships, due each year in March. There is a downloadable application with fill-in blanks to make it easier.
Do You Know Someone Deserving of an ICTM Award?
ILLINOIS COUNCIL OF TEACHERS OF MATHEMATICS
SCHOLARSHIPS IN MATHEMATICS EDUCATION
Maria Christina Gianni
Amy Wieting
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ICTM 2015 Award Recipients, pictured at left:Left to right: Tina Novella, Richard Kaplan, Leona Mirza, Martha Reilly, Peter Braunfeld, Martha Eggers, Danyel Larsen
ICTM 2015 Scholarship Recipients, pictured at right:Maria-Christina Gianna, University of Illinois at Urbana-Champaignand Amy Weiting, Illinois State University
ICTM 2015 New Board Officers, pictured at left:Left to right: Jeremy Babel, Director 9-12, Denise Brown, Director EC-6,Sendhil Revuluri, Director At-Large
Your ICTM Board of Directors, pictured at right:
Front: Eric Bright, Sendhil Revuluri, Martin Funk, Zach Herrmann
Middle: Lannette Jennings, Anita Reid, Carly Morales, Denise Brown
Back: Bob Mann, Jackie Murawska, Jeremy Babel, Adam Poetzel (retired) and President George Reese
Not pictured: Craig Cullen and Peter Wiles
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CONFERENCE CORNERICTM 65th Annual Conference:
WOW, what an event! Thank you to all who attended the ICTM 65th Annual Conference. Jo Boaler and Eli Luber-off gave a dynamic start to two days of professional de-velopment, networking and engagement to reinvigorate your math teaching. We hope you enjoyed the event as much as we did!
If you missed this year’s ICTM Annual Conference, mark your calendar and start planning now to attend next Oc-tober 7-8, 2016, when we return to Peoria. Stay tuned to www.ICTM.org for updates and breaking news on highly-anticipated Guest Speakers for the 2016 Annual Conference!
TELL US WHAT YOU THOUGHT!If you haven’t already responded to an email invitation to complete a conference survey,
you can do it now at http://eiu.co1.qualtrics.com/SE/?SID=SV_eOMbNRJn89Ca5UN
Call for Speakers:
Take Advantage of the Opportunity to Present!
66th Annual ICTM ConferenceOctober 7-8, 2016, Peoria, IL
In 2016 the ICTM annual conference will be held at the Hotel Pere Marquette in Peoria, IL. Mathematics education has encountered considerable change in recent times and ICTM is here to provide comprehensive effective insights, practices, and activities to effectively deal with these changes.
Please consider joining over 100 other mathematics professionals who are presenting either a 60-minute talk or a 90-minute workshop in Tinley Park. A featured speaker will provide a keynote presentation to open the conference on Friday morning. Presentations and workshops will follow.
Be part of this exciting program and contribute to the mathematics education profession by visiting the ICTM website (http://www.ictm.org).
Deadline for proposal submission is March 15, 2016
Access the Speaker Proposal Form at : http://www.ictm.org/SpeakerProposal.htm.
Be a part of this great event. Submit your proposal today!
What’s MATH Got to Do With It?
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I.C.T.M. Bulletin December 2015: Submitted by Jackie Murawska, ICTM Director-at-Large/ Board Chair, Grades 2-12
I.C.T.M. Bulletin December 2015: Submitted by Jackie Murawska, ICTM Director-at-Large/ Board Chair, Grades 2-12
Introduction to KenKen Puzzles
What is KenKen? KenKen is a puzzle similar to Sudoku. It was invented in 2003 by a Japanese mathematics instructor named Tetsuya Miyamoto. KenKen is a Japanese word for “square wisdom” or “cleverness squared.” Here are the rules:
1. Each square can only contain a single number. In a 3×3 grid, use numbers 1-3. In a 4×4 grid, use numbers 1-4, etc.
2. The numbers cannot be repeated in any row or any column. 3. In any cage, set of squares outlined in bold, the digits must combine, in any order, to create the
target number using the specified mathematical operation (+, −, ×, ÷). If there is no operator, just fill in the number provided.
Let’s try some! Remember never to guess. If you’re not sure, put your choices, called candidates, into a square. For example, in either 4×4 grid below, the candidates for the cage labeled 7+ would be 3 and 4.
KenKen puzzles above courtesy of www.kenkenpuzzles.com
Want more KenKen? You can play anytime for free on the KenKen site www.kenkenpuzzles.com,
your teacher can sign up for the free weekly teacher packet through the KenKen site, you can purchase a KenKen paperback puzzle book on Amazon, or you can download a KenKen app on your smart phone. Enjoy!
Remember: never guess!
A number can be
repeated in a cage.
Doubles strategy:
put in candidates
Where’s a good place to start?
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Share and Share Alike?Income (In)equality & the Gini Coefficient
The Gini coefficient is a measure of (in)equality in distributions. This task allows students to use visual representations and statistical reasoning to explore how the Gini coefficient works, and apply it to real-world data. The task provokes cognitively demanding problem-solving (SMP1) and reasoning (SMP3) while integrating prior mathematical content (proportional reasoning, graphing, calculating area) with a heavy dose of mathematical modeling (SMP4). The task is most appropriate for high school students, especially in geometry and beyond. It is best done as a two- or three-period activity, with the first period focused on the introductory exercises to help build students’ intuition, and the rest to explore using real data. Tools (spreadsheet programs, graph paper, etc.) can be helpful. A longer description, with additional context (and editable to make handouts), and spreadsheets for the intro exercises, are online at http://goo.gl/3sd00w.
You may have heard about income inequality in the news. But what makes distributions of income more or less equal? And how is that even measured? In this task, you’ll use the tools of mathematics to analyze the equality – or inequality – of distributions of income. You’ll start with tools you know (statistics, graphing, area), and then practice using a new tool called the Gini coefficient. Finally, you’ll apply all of your tools and problem-solving skills to real data.
Introductory Exercises (recommend students work these in pairs, with a discussion following)
Suppose we’re examining the distribution of income in a village of ten people.There are some basic steps that will help us analyze the distribution and draw conclusions:1. Find the total income, and express each person’s income as a share (percentage of total)2. Put these income shares in order from least to greatest, then put them in a table3. Find the cumulative share of income, up to and including each person4. Graph these cumulative income shares against the number of people (see spreadsheets)
Work with your partner to try these five examples to give you a sense of different possibilities.
1. Every person earns $50,000. What is the average income? What does the graph look like? This is an example of perfect income equality.
2. One person earns $500,000 and the other nine earn nothing. What is the average income? What does the graph look like? This is an example of near-perfect income inequality.
3. Suppose every person earns $50,000, and then one gets a raise to $300,000. What is the new average income? How many people actually benefited from this change? What does the graph look like? Where is it relative to the first and second graphs?
4. Suppose the one person’s raise to $300,000 came out of the others’ incomes, so that the average income remains $50,000. What is the new income of the other nine people? What does the graph look like? Where is it relative to the first and second graphs?
5. Suppose the ten incomes are (in thousands) 32, 36, 40, 44, 48, 52, 56, 60, 64, and 68. What is the average income? How does the highest earner’s income compare to the lowest earner’s income? What does the graph look like? Where is it relative to the first and second graphs?
[After the discussion, these definitions set students up for the deeper investigation to follow.]
These graphs are called called Lorentz curves, and let you see the distribution of income in the village. The same tool can show the distribution of income in an entire country by lumping people together into ten income bands, or deciles, and doing the same
I.C.T.M. Bulletin December 2015: Submitted by Sendhil Revuluri, ICTM Director-at-Large
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I.C.T.M. Bulletin December 2015: Submitted by Sendhil Revuluri, ICTM Director-at-Large
calculations and making the same graphs.1 Note that the Lorentz curve is always between the first two curves (the straight diagonal line for perfect equality, and the very kinked graph for perfect inequality).
The Gini coefficient is a way to measure income inequality by turning the Lorentz curve into a single number. It is calculated as a ratio of areas:
area between the Lorentz curve and the curve for perfect equality——————————————————————————————
area between the curve for perfect equality and zero
Calculate the Gini coefficient for each of the five income distributions from parts 1–5 above. (Keep your work on these exercises; it will help you when you work with real data next.)
[The longer description online has some additional guidance on finding areas, as well as a few different options for the deeper investigation, depending on how much time you have for it.]
Deeper Investigation (recommend students do this stage in pairs or small groups)
You will now work to analyze income distributions from real data from real countries.1. Select two countries you want to investigate. Explain why you chose these two.
2. What is your best guess about what you will find about their income inequality? Use your knowledge of world events and economics to explain your reasoning.
3. In your own words, briefly restate how the Gini coefficient measures income inequality.4. Retrieve income data at https://www.wider.unu.edu/data.2 Pick a year for each country.5. Use the method of the introductory exercises to construct Lorentz curves for each country.6. Calculate Gini coefficients for each country and time. (If your initial method doesn’t work as well as you’d like, modify your
method as needed and think about using technology.)7. Describe basic patterns or trends you found and summarize the results of your research. Was your initial best guess supported
by your research or analysis? Explain why or why not.
Possible Discussions and Extensions
You can discuss some important mathematical ideas (visual representations, strategies for finding areas, how ratios are used as measures, etc.) when students work on the introductory exercises. Once students complete the deeper investigation, there are more directions you could go. Students’ data could be pooled to try to draw more general conclusions, or students could continue with their investigation with deeper questions, such as:
· What happens to the Gini coefficient when all incomes double?· Would your results be the same if you used only five income bands? Only three? If you used twenty? Or one hundred?
Or if each individual person was split out?· What are the good and bad features of the Gini coefficient as a measure?· Are there other measures of inequality you could devise? When is each measure better, more appropriate, or more
informative?· What if incomes are redistributed? What schemes could reduce inequality and still get the support of most of the
population? Are these fair?· Which is more important, the average income or the inequality of income?· What income distribution is “right”? (Note that incomes differ for many reasons, including age, education, cost-of-living,
and effort, as well as race, wealth, and historical patterns of advantage or disadvantage.)
Some of these questions are more mathematical than others (and some are still the topic of active social science research), but all are further directions in which students could continue.
1 Academic analyses usually use unit record data (individual people). To make the task more accessible for students without needing a lot of “mechanics” or technology, this task uses decile data (tenths of the population). (The adjustments for this change are intentionally ignored here; they’re subtle and won’t affect students’ conclusions.)2 The database also includes calculated Gini coefficients. You may want to let students see these, or not; they are helpful to quickly identify (potentially frustrating) student computational errors, or to diagnose misconceptions.
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Directors: Anita Reid/Martin FunkSubmissions from:
Reports: Eric Bright Martin Funk Jackie Murawska Robert Mann
George Reese Randy & Sue PippenActivities: Jackie Murawska Sendhil RevuluriConference Info: Marshall Lassak
Produced by: Eastern Illinois University School of Continuing Education
ICTM
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Please contact any of the following ICTM board members if you have any questions or concerns:
PresidentGeorge ReeseMSTE Office505 East Green StreetChampaign, IL [email protected]
Board ChairJackie MurawksaSaint Xavier University3700 West 103rd StreetChicago, IL [email protected]
Conference DirectorMarshall Lassak [email protected]
Your ICTM Board RepresentativesGeorge Reese (2015–17)PresidentUniversity of Illinois-MSTE
George Reese (2014–15)President-ElectUniversity of Illinois - MSTE
Marshall Lassak Conference CoordinatorEastern IL University
Jackie Murawska (2013–16)Board ChairSaint Xavier University
Sendhil Revuluri (2015–18)Director-at-LargeUniversity of Illinois at U-C
Zachary Herrmann (2014–17)Director-at-LargeEvanston Township High School
Craig Cullen (2013–16)Director, University/ Community CollegeIllinois State University
Peter Wiles (2014–17)Director, University/ Community College Eastern Illinois University
Martin Funk (2013–16)Director 9–12New Trier High School
Jeremy Babel (2015–18)Director 9-12Leyden HS
Anita Reid (2014–16)Director 5–8Lewistown Central High School
Eric Bright (2014–17)Director 5–8Charleston Middle School
Carly Morales (2014–17)Director EC–6Regional Office of Education #38
Denise Brown (2015–18)Director EC–6Carruthers Elementary School
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CALL FOR ARTICLESCan you help?
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If you would like to volunteer as a reviewer or have an article to submit, please contact
the editors at [email protected].
We look forward to hearing from you.
11
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ICTM Spring Regional Conferences Southern Illinois University at Carbondale Thursday, February 18, 2016 Western Illinois University, Macomb Friday, April 8, 2016
NCSM Annual ConferenceSan Francisco, CA
April 11-13, 2016
NCTM 2015 Annual Meeting and Conference San Francisco, CA
April 13-15, 2016
ICTM 2016 Math ContestUniversity of Illinois at Urbana-Champaign
May 7, 2016